Each transaction has an accumulated weight which expresses the necessary effort to void the transaction in case of a double-spending, similar to the number of confirmations in Bitcoin. A transaction is confirmed when its accumulated weight surpasses a given threshold.
When a new block or transaction arrives, it increases the accumulated weight of all verified transactions, increasing the confirmation certainty of all of them.
For instance, in the above DAG of transactions, transaction f767 is directly verifying transactions 2050 and 1b76, and indirectly verifying transactions 0278, d59b, 41b0, 5be4, 977d, and 207a. Transaction f767 increases the accumulated weight of all these transactions.
As blocks arrive in a regular pace — every minute, on average — , they regularly increase previous transactions’ accumulated weight, eventually confirming them. Thus, the confirmation time will never be higher than the time to find six consecutive blocks, exactly like in Bitcoin.
However, when many new transactions are also arriving, they are also increase previous transactions’ accumulated weight, which speeds up the confirmation, reducing the confirmation time. If the number of new transactions is significantly high, they can confirm previous transactions even before a new block is found, i.e., there will be only transactions confirming transactions.
Therefore, the network benefits from a high number of transactions. When the number of new transactions is low, the confirmations are mostly made by the blocks, just like in Bitcoin. But, as the number of new transactions increases, transactions also contribute to other transactions confirmation, making them confirm faster. In this case, Hathor’s dynamics diverges from Bitcoin’s.
